Details

analyze229.0ms (3.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample65.0ms (1%)

Algorithm

1×

intervals

Results

26.0ms	59×	body	1024	valid
12.0ms	145×	body	128	valid
8.0ms	31×	body	512	valid
6.0ms	5×	body	2048	valid
3.0ms	16×	body	256	valid
1.0ms	7×	body	128	invalid
0.0ms	1×	body	1024	invalid
0.0ms	3×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify226.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4933	41
1	4933	41

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 27.8b

Counts

2 → 1

Compiler

Compiled 112 to 96 computations (14.3% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
1.5b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite72.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_432`
78×	`exp-neg_binary64_470`
76×	`frac-times_binary64_433`
59×	`exp-diff_binary64_471` `neg-sub0_binary64_418`
38×	`associate-r/_binary64_365` `associate-l/_binary64_366`
30×	`flip-+_binary64_397` `flip3-+_binary64_426`
28×	`flip3--_binary64_427` `flip--_binary64_398`
19×	`un-div-inv_binary64_421`
12×	`exp-prod_binary64_475`
11×	`*-un-lft-identity_binary64_423`
10×	`add-sqr-sqrt_binary64_445` `add-log-exp_binary64_462`
8×	`add-cube-cbrt_binary64_458`
6×	`pow1_binary64_484` `add-cbrt-cube_binary64_459`
5×	`associate-l_binary64_364` `add-exp-log_binary64_461`
4×	`rem-exp-log_binary64_463`
3×	`associate-r_binary64_363`
2×	`neg-log_binary64_516` `distribute-lft-out_binary64_374` `distribute-lft-neg-in_binary64_380` `neg-mul-1_binary64_419` `distribute-rgt-neg-in_binary64_381`
1×	`pow-prod-down_binary64_494` `sub-neg_binary64_416` `diff-log_binary64_515` `cancel-sign-sub-inv_binary64_389` `prod-exp_binary64_472` `*-commutative_binary64_354` `div-inv_binary64_420` `unswap-sqr_binary64_391` `cbrt-unprod_binary64_456`

Counts

4 → 156

Calls

4 calls:

21.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
14.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

series384.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
53.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
38.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
31.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

simplify167.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4953	8651
1	4953	8651

prune1.3s (18.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	4	169

Merged error: 0.0b

Counts

169 → 4

Compiler

Compiled 24669 to 19920 computations (19.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (*.f64 2/3 (pow.f64 x 3)) 2)
0.1b	(*.f64 2/3 (pow.f64 x 3))
7.8b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_445`
12×	`associate-r_binary64_363`
10×	`add-log-exp_binary64_462`
8×	`add-exp-log_binary64_461`
7×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
5×	`add-cbrt-cube_binary64_459`
4×	`cube-prod_binary64_451` `unswap-sqr_binary64_391` `unpow-prod-down_binary64_502`
3×	`associate-l_binary64_364` `prod-exp_binary64_472` `pow1_binary64_484`
2×	`diff-log_binary64_515` `sqr-pow_binary64_395` `sum-log_binary64_514`
1×	`associate--l+_binary64_360` `sub-neg_binary64_416` `pow-to-exp_binary64_492` `flip-+_binary64_397` `unpow3_binary64_489` `cancel-sign-sub-inv_binary64_389` `+-commutative_binary64_353` `pow-exp_binary64_491` `flip3--_binary64_427` `*-commutative_binary64_354` `flip3-+_binary64_426` `difference-of-squares_binary64_392` `cube-mult_binary64_453` `flip--_binary64_398` `cbrt-unprod_binary64_456`

Counts

3 → 57

Calls

3 calls:

9.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
7.0ms	(*.f64 2/3 (pow.f64 x 3))
6.0ms	(+.f64 (*.f64 2/3 (pow.f64 x 3)) 2)

series188.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

104.0ms	(+.f64 (*.f64 2/3 (pow.f64 x 3)) 2)
49.0ms	(*.f64 2/3 (pow.f64 x 3))
34.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify97.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4988	860
1	4988	860

prune68.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

Compiler

Compiled 1251 to 924 computations (26.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (*.f64 (-.f64 1 eps) x))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
3.2b	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_423`
15×	`times-frac_binary64_429` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
12×	`add-log-exp_binary64_462`
9×	`frac-sub_binary64_432`
8×	`distribute-lft-out_binary64_374`
7×	`exp-prod_binary64_475`
6×	`add-cbrt-cube_binary64_459`
5×	`exp-neg_binary64_470` `add-exp-log_binary64_461` `div-inv_binary64_420` `associate-/l*_binary64_368`
4×	`frac-times_binary64_433` `exp-diff_binary64_471` `neg-sub0_binary64_418` `pow1_binary64_484` `flip3--_binary64_427` `flip--_binary64_398`
3×	`rem-exp-log_binary64_463` `associate-/r*_binary64_367`
2×	`diff-log_binary64_515` `exp-to-pow_binary64_485` `associate-r/_binary64_365` `associate-/l/_binary64_370` `associate-l/_binary64_366`
1×	`sub-neg_binary64_416` `flip-+_binary64_397` `un-div-inv_binary64_421` `neg-log_binary64_516` `cancel-sign-sub-inv_binary64_389` `distribute-lft-neg-in_binary64_380` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `neg-mul-1_binary64_419` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `distribute-rgt-neg-in_binary64_381`

Counts

4 → 86

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))))
12.0ms	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
5.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
3.0ms	(exp.f64 (*.f64 (-.f64 1 eps) x))

series496.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

351.0ms	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))))
80.0ms	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
37.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
28.0ms	(exp.f64 (*.f64 (-.f64 1 eps) x))

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5025	2750

prune197.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	99	3	102

Merged error: 0.0b

Counts

102 → 3

Compiler

Compiled 3851 to 3045 computations (20.9% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 -1) (*.f64 (+.f64 1 eps) x))
0.0b	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (*.f64 (-.f64 1 eps) x))
3.2b	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (*.f64 (+.f64 1 eps) x))))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_423`
16×	`add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
15×	`times-frac_binary64_429`
10×	`add-log-exp_binary64_462`
8×	`distribute-lft-out_binary64_374`
6×	`add-cbrt-cube_binary64_459`
5×	`pow1_binary64_484` `add-exp-log_binary64_461` `div-inv_binary64_420` `associate-/l*_binary64_368`
4×	`pow-pow_binary64_495` `exp-prod_binary64_475`
3×	`associate-/r*_binary64_367` `unpow-prod-down_binary64_502`
2×	`diff-log_binary64_515` `exp-to-pow_binary64_485` `flip3--_binary64_427` `associate-/l/_binary64_370` `associate-*l/_binary64_366` `flip--_binary64_398` `frac-sub_binary64_432`
1×	`sub-neg_binary64_416` `pow-to-exp_binary64_492` `flip-+_binary64_397` `cancel-sign-sub-inv_binary64_389` `pow-exp_binary64_491` `rem-exp-log_binary64_463` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434` `pow-unpow_binary64_500` `cbrt-undiv_binary64_457` `sqr-pow_binary64_395` `div-exp_binary64_474`

Counts

4 → 80

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (*.f64 (+.f64 1 eps) x))))
12.0ms	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
4.0ms	(pow.f64 (exp.f64 -1) (*.f64 (+.f64 1 eps) x))
3.0ms	(exp.f64 (*.f64 (-.f64 1 eps) x))

series455.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

287.0ms	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (*.f64 (+.f64 1 eps) x))))
90.0ms	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
50.0ms	(pow.f64 (exp.f64 -1) (*.f64 (+.f64 1 eps) x))
28.0ms	(exp.f64 (*.f64 (-.f64 1 eps) x))

simplify113.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4995	2397
1	4995	2397

prune188.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Merged error: 0.0b

Counts

95 → 3

Compiler

Compiled 3556 to 2789 computations (21.6% saved)

regimes54.0ms (0.8%)

Compiler: Compiled 148 to 134 computations (9.5% saved)

bsearch89.0ms (1.3%)

Steps

Iters	Range		Point
10	2.3446147012439161e-07	1891661.7461051005	61.83415131857526

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	189	68
1	189	68

end0.0ms (0%)

sample2.1s (31.2%)

Algorithm

1×

intervals

Results

865.0ms	1970×	body	1024	valid
358.0ms	4277×	body	128	valid
275.0ms	1080×	body	512	valid
161.0ms	205×	body	2048	valid
74.0ms	468×	body	256	valid
18.0ms	205×	body	128	invalid
14.0ms	183×	body	128	overflowed
8.0ms	18×	body	1024	invalid
4.0ms	12×	body	512	invalid
2.0ms	8×	body	256	invalid

Compiler

Compiled 147 to 128 computations (12.9% saved)

Details

analyze229.0ms (3.4%)

sample65.0ms (1%)

simplify226.0ms (3.4%)

prune8.0ms (0.1%)

localize21.0ms (0.3%)

rewrite72.0ms (1.1%)

series384.0ms (5.7%)

simplify167.0ms (2.5%)

prune1.3s (18.8%)

localize8.0ms (0.1%)

rewrite26.0ms (0.4%)

series188.0ms (2.8%)

simplify97.0ms (1.4%)

prune68.0ms (1%)

localize17.0ms (0.3%)

rewrite51.0ms (0.8%)

series496.0ms (7.4%)

simplify70.0ms (1%)

prune197.0ms (2.9%)

localize22.0ms (0.3%)

rewrite48.0ms (0.7%)

series455.0ms (6.8%)

simplify113.0ms (1.7%)

prune188.0ms (2.8%)

regimes54.0ms (0.8%)

bsearch89.0ms (1.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.1s (31.2%)

Profiling